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Abstract:

In this study we present the results of an attempt to experimentally measure the energy decay in wind-tunnel grid turbulence. We show that it is possible to unambiguously determine the energy decay exponent, but departures of the turbulence from the ideas of homogeneity and isotropy mean it is not possible to compare our results to the theoretical predictions. Integral invariants have also recently been predicted to exist in two-dimensional turbulence. There are three canonical cases: E(k → 0) ~ Jk-1, E(k → 0) ~ Lk and E(k → 0) ~ Ik3. We perform direct numerical simulations in large domains and demonstrate that, in line with the theoretical predictions, J and L are invariants whilst I is strongly time-dependent. In addition, we show that the large scales of E ~ Jk-1 and E ~ Ik3 turbulence evolve in an almost self-similar manner, whilst the evolution of E ~ Lk turbulence cannot be self-similar due to the strong inverse energy cascade. We also extend the analysis to the case of quasi-geostrophic shallow-water turbulence, where we show that there are two further canonical cases, E ~ Mk5 and E ~ Nk7. In this system I and M are invariants, whilst N is time-dependent. We confirm thee predictions with numerical simulations and show that, unlike strictly two-dimensional turbulence, there are no long-range triple correlations in QGSW turbulence.